Project, Assignment - ‫ﺻﻔﺤﻪ ١‬...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ‫ﺻﻔﺤﻪ ١‬ ‫ﺭﻭﺷﻬﺎﯼ ﺗﺤﻠﻴﻞ ﺣﻠﻘﻪ ﻭ ﮐﺎﺕ ﺳﺖ‬ ‫ﻓﺼﻞ ﺳﻮﻡ‬ ‫١ ‐ ﺩﺭ ﺷﮑﻞ ﺍﻟﻒ ﻣﻘﺎﺑﻞ ﻣﺪﺍﺭﯼ ﺑﺎ ٦ ﺷﺎﺧﻪ ﺑﺎ ﮔﺮﺍﻑ ﻣﻄﺎﺑﻖ‬ ‫ﺷﮑﻞ ﺏ ﻣﺸﺨﺺ ﺷﺪﻩ ﺍﺳﺖ . ﻣﯽ ﺧﻮﺍﻫﻴﻢ ﻣﺪﺍﺭ ﺭﺍ ﺑﻪ‬ ‫ﺭﻭﺵ ﺗﺤﻠﻴﻞ ﺣﻠﻘﻪ ﺗﺤﻠﻴﻞ ﻧﻤﺎﻳﻴﻢ . ﺩﺭﺧﺖ )٤،٥،٦(‬ ‫ﺭﺍ ﺑﺮﺍﯼ ﺍﻳﻦ ﻣﻨﻈﻮﺭ ﺍﻧﺘﺨﺎﺏ ﻣﯽ ﻧﻤﺎﻳﻴﻢ :‬ ‫ﺍﻟﻒ _ ﻣﻌﺎﺩﻻﺕ ‪ KVL‬ﺑﺮﺍﯼ ﺣﻠﻘﻪ ﻫﺎﯼ ﺍﺳﺎﺳﯽ ﺑﻪ ﺻﻮﺭﺕ‬ ‫ﻭﻟﺘﺎﮊ‬ ‫ﻣﺎﺗﺮﻳﺴﯽ ‪ Bv=o‬ﺑﻨﻮﻳﺴﻴﺪ . ﺑﺮﺩﺍﺭ ‪ v‬ﺑﺮﺩﺍﺭ‬ ‫ﺷﺎﺧﻪ ﻫﺎ ﻣﯽ ﺑﺎﺷﺪ .‬ ‫ﺏ _ ﻣﻌﺎﺩﻻﺕ ‪ kcl‬ﺭﺍ ﺑﺼﻮﺭﺕ ﻣﺎﺗﺮﻳﺴﯽ ‪ j=BTi‬ﺑﻨﻮﻳﺴﻴﺪ‬ ‫. ﺑﺮﺩﺍﺭ ‪ j‬ﺑﺮﺩﺍﺭﺟﺮﻳﺎﻥ ﺷﺎﺧﻪ ﻫﺎ ﻭﺑﺮﺩﺍﺭ‪ i‬ﺑﺮﺩﺍﺭ ﺟﺮﻳﺎﻥ‬ ‫ﺣﻠﻘﻪ ﻫﺎ )ﻟﻴﻨﮏ ﻫﺎ( ﺍﺳﺖ .‬ ‫ﭖ _ ﺑﺮﺍﯼ ﻫﺮ ﻳﮏ ﺍﺯ ﺷﺎﺧﻪ ﻫﺎ ﺑﺎ ﺷﻤﺎﺭﻩ ﻫﺎﯼ ﻣﺸﺨﺺ ﺷﺪﻩ ﺩﺭ ﺷﮑﻞ‬ ‫ﺍﻟﻒ ، ﻣﻌﺎﺩﻟﻪ ﺷﺎﺧﻪ ﺭﺍ ﺑﻨﻮﻳﺴﻴﺪ ﻭ ﺁﻧﻬﺎ ﺭﺍ ﺑﺼﻮﺭﺕ ﻣﺎﺗﺮﻳﺴﯽ‬ ‫‪ v=Rj-Rjs+vs‬ﺩﺭ ﺁﻭﺭﻳﺪ . ﻣﺎﺗﺮﻳﺲ ‪ R‬ﻳﮏ ﻣﺎﺗﺮﻳﺲ ﻣﺮﺑﻌﯽ‬ ‫٦ * ٦ ﻭ ﻏﻴﺮ ﻣﺘﻘﺎﺭﻥ )ﺑﻪ ﻋﻠﺖ ﻭﺟﻮﺩ ﻣﻨﺎﺑﻊ ﻭﺍﺑﺴﺘﻪ ( ﻣﯽ ﺑﺎﺷﺪ .‬ ‫ﺕ _ ﺑﺎ ﺣﺬﻑ ﺑﺮﺩﺍﺭﻫﺎﯼ ‪v‬ﻭ‪ j‬ﻣﻌﺎﺩﻻﺕ ﻗﺴﻤﺖ ﻫﺎﯼ ﺍﻟﻒ ، ﺏ ﻭ ﭖ ﺑﻪ‬ ‫ﻣﻌﺎﺩﻻﺕ ‪ Zl i=es‬ﺑﺮﺳﻴﺪ .‬ ‫ﺙ _ ﺣﺎﻝ ﻣﯽ ﺧﻮﺍﻫﻴﻢ ﺑﻪ ﺭﻭﺵ ﻧﻈﺮﯼ )ﺑﺪﻭﻥ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﺎﺗﺮﻳﺲ‬ ‫ﺣﻠﻘﻪ ﻫﺎﯼ ﺍﺳﺎﺳﯽ‪( B‬ﺑﻪ ﻣﻌﺎﺩﻻﺕ ﻗﺴﻤﺖ ﺕ ﺑﺮﺳﻴﻢ . ﺍﺑﺘﺪﺍ‬ ‫ﻣﻨﺎﺑﻊ ﺟﺮﻳﺎﻥ) ﻧﺎﺑﺴﺘﻪ ﻭ ﻭﺍﺑﺴﺘﻪ( ﺭﺍ ﺑﻪ ﻣﻨﺎﺑﻊ ﻭﻟﺘﺎﮊ ﺗﺒﺪﻳﻞ ﻧﻤﺎﻳﻴﺪ‬ ‫ﻭ ﻣﻌﺎﺩﻻﺕ ‪ Zli=es‬ﺭﺍ ﻧﺘﻴﺠﻪ ﺑﮕﻴﺮﻳﺪ ﻭﺍﻳﻦ ﻣﻌﺎﺩﻻﺕ ﺭﺍ ﺣﻞ‬ ‫ﻧﻤﺎﻳﻴﺪ ﻭ ﺑﺮﺩﺍﺭ ‪ i‬ﺭﺍ ﻣﺤﺎﺳﺒﻪ ﻧﻤﺎﻳﻴﺪ ﻭ ﺍﺯ ﺁﻥ ‪ va‬ﻭ‪ vb‬ﻭ‪ v c‬ﺭﺍ‬ ‫ﻣﺸﺨﺺ ﻧﻤﺎﻳﻴﺪ .‬ ‫٢‐ ﺩﺭ ﺷﮑﻞ ﺍﻟﻒ ﻣﻘﺎﺑﻞ ﻣﺪﺍﺭﯼ ﺑﺎ ٥ ﺷﺎﺧﻪ ﺑﺎ ﮔﺮﺍﻑ ﻣﻄﺎﺑﻖ ﺷﮑﻞ ﺏ‬ ‫ﻣﺸﺨﺺ ﺷﺪﻩ ﺍﺳﺖ . ﻣﯽ ﺧﻮﺍﻫﻴﻢ ﻣﺪﺍﺭ ﺭﺍ ﺑﻪ ﺭﻭﺵ ﺗﺤﻠﻴﻞ ﮐﺎﺕ‬ ‫ﺳﺖ ﺗﺤﻠﻴﻞ ﻧﻤﺎﻳﻴﻢ . ﺑﺮﺍﯼ ﺍﻳﻦ ﻣﻨﻈﻮﺭ ﺩﺭﺧﺖ )٥،٤،٣( ﺭﺍ‬ ‫ﺍﻧﺘﺨﺎﺏ ﻣﯽ ﻧﻤﺎﻳﻴﻢ:‬ ‫ﺍﻟﻒ _ ﻣﻌﺎﺩﻻﺕ ‪ KCL‬ﺑﺮﺍﯼ ﮐﺎﺕ ﺳﺖ ﻫﺎﯼ ﺍﺳﺎﺳﯽ ﺑﺼﻮﺭﺕ ‪Qj=o‬‬ ‫ﺑﻨﻮﻳﺴﻴﺪ.‬ ‫ﺏ _ ﻣﻌﺎﺩﻻﺕ ‪ KVL‬ﺭﺍ ﺑﺼﻮﺭﺕ ﻣﺎﺗﺮﻳﺲ ‪ v=Q e‬ﺑﻨﻮﻳﺴﻴﺪ. ﺑﺮﺩﺍﺭ‬ ‫‪ e‬ﺑﺮﺩﺍﺭ ﻭﻟﺘﺎﮊ ﺷﺎﺧﻪ ﻫﺎﯼ ﺩﺭﺧﺖ ﺍﺳﺖ.‬ ‫ﭖ _ ﻣﻌﺎﺩﻻﺕ ﺷﺎﺧﻬﺎ ﺭﺍ ﺑﺼﻮﺭﺕ ﻣﺎﺗﺮﻳﺴﯽ ‪ j=Gv-Gvs+js‬ﺑﻨﻮﻳﺴﻴﺪ.‬ ‫‪T‬‬ ‫ﺻﻔﺤﻪ ٢‬ ‫ﺭﻭﺷﻬﺎﯼ ﺗﺤﻠﻴﻞ ﺣﻠﻘﻪ ﻭ ﮐﺎﺕ ﺳﺖ‬ ‫ﻓﺼﻞ ﺳﻮﻡ‬ ‫ﺕ _ ﺑﺎ ﺣﺬﻑ ﺑﺮﺩﺍﺭﻫﺎﯼ ‪v‬ﻭ‪ j‬ﻣﻌﺎﺩﻻﺕ ﻗﺴﻤﺖ ﻫﺎﯼ ﺍﻟﻒ ﻭ ﺏ ﻭ ﭖ‬ ‫ﺑﺎﻻ، ﻣﻌﺎﺩﻻﺕ ‪ Y q e=i s‬ﺭﺍ ﻧﺘﻴﺠﻪ ﺑﮕﻴﺮﻳﺪ .‬ ‫ﺙ _ ﻣﻌﺎﺩﻻﺕ ﮔﺮﻩ ﺭﺍ ﺑﻪ ﺭﻭﺵ ﻧﻈﺮﯼ )ﺑﺪﻭﻥ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﻣﺎﺗﺮﻳﺲ‬ ‫ﮐﺎﺗﺴﺖ ﻫﺎﯼ ﺍﺳﺎﺳﯽ ‪ (Q‬ﻭ ﺑﺎ ﺣﻞ ﺁﻥ ﺑﺮﺩﺍﺭ ‪ e‬ﺭﺍ ﻣﺤﺎﺳﺒﻪ ﻭ‬ ‫ﻣﻘﺎﺩﻳﺮ ‪ v1 ,vx‬ﺭﺍ ﻧﺘﻴﺠﻪ ﺑﮕﻴﺮﻳﺪ . )‪ v‬ﻭﻟﺘﺎﮊ ﺷﺎﺧﻪ ١ ، ﺩﺭ ﺟﻬﺖ‬ ‫ﻗﺮﺍﺭﺩﺍﺩﯼ ﻣﺘﻨﺎﻇﺮ ﺑﺎ ﺟﺮﻳﺎﻥ ﺍﺳﺖ .(‬ ‫٣ – ﮐﺪﺍﻣﻴﮏ ﺍﺯ ﺭﻭﺵ ﻫﺎﯼ ﺗﺤﻠﻴﻞ ﺣﻠﻘﻪ ﻳﺎ ﮐﺎﺕ ﺳﺖ ﺭﺍ ﺑﺮﺍﯼ ﺗﺤﻠﻴﻞ‬ ‫ﻣﺌﺎﺭ ﻣﻘﺎﺑﻞ ﻣﻨﺎﺳﺐ ﺗﺮ ﻣﯽ ﺩﺍﻧﻴﺪ ؟ ﭼﺮﺍ ؟ ﺑﺮﺍﯼ ﺩﺭﺧﺖ ﻣﺸﺨﺺ‬ ‫ﺷﺪﻩ ، ﻣﻌﺎﺩﻻﺕ ﺍﻧﺘﮕﺮﺍﻝ ﺩﻳﻔﺮﺍﻧﺴﻴﻞ ﺣﻠﻘﻪ ‪ Z1(D)i =es‬ﺭﺍ‬ ‫ﺑﻨﻮﻳﺴﻴﺪ ﻭ ﺷﺮﺍﻳﻂ ﺍﻭﻟﻴﻪ ﻻﺯﻡ ﺑﺮﺍﯼ ﺣﻞ ﺁﻥ ﺭﺍ ﺑﺮﺣﺴﺐ ﻣﺸﺨﺺ‬ ‫ﻧﻤﺎﻳﻴﺪ.‬ ‫٤‐ ﮐﺪﺍﻣﻴﮏ ﺍﺯ ﺭﻭﺵ ﻫﺎﯼ ﺗﺤﻠﻴﻞ ﺣﻠﻘﻪ ﻭ ﮐﺎﺕ ﺳﺖ ﺭﺍ ﺑﺮﺍﯼ ﺗﺤﻠﻴﻞ‬ ‫ﻣﺪﺍﺭ ﻣﻘﺎﺑﻞ ﻣﻨﺎﺳﺐ ﺗﺮ ﻣﯽ ﺩﺍﻧﻴﺪ ؟ ﭼﺮﺍ ؟ ﺁﻳﺎ ﭘﺎﺳﺦ ﺷﻤﺎ‬ ‫ﺑﺴﺘﮕﯽ ﺑﻪ ﺩﺭﺧﺖ ﺍﻧﺘﺨﺎﺏ ﺷﺪﻩ ﺩﺍﺭﺩ ؟ ﻣﻌﺎﺩﻻﺕ ﺍﻧﺘﮕﺮﺍﻝ‬ ‫ﺩﻳﻔﺮﺍﻧﺴﻴﻞ ﮐﺎﺕ ﺳﺖ ‪ Yq e=is‬ﺭﺍ ﺑﺮﺍﯼ ﺩﺭﺧﺖ ﻣﺘﺸﮑﻞ ﺍﺯ‬ ‫ﺧﺎﺯﻥ ﻭ ﻣﻘﺎﻭﻣﺖ ٢ ﺍﻫﻤﯽ ﺑﻨﻮﻳﺴﻴﺪ ﻭ ﺷﺮﺍﻳﻂ ﺍﻭﻟﻴﻪ ﻻﺯﻡ ﺑﺮﺍﯼ‬ ‫ﺣﻞ ﺁﻥ ﺭﺍ ﻣﺸﺨﺺ ﻧﻤﺎﺋﻴﺪ ﺍﺯ ﺍﻳﻦ ﻣﻌﺎﺩﻻﺕ، ﻣﻌﺎﺩﻻﺕ ﮐﺎﺕ ﺳﺖ‬ ‫‪ YqE=Is‬ﺩﺭ ﺣﺎﻟﺖ ﺩﺍﺋﻤﯽ ﺳﻴﻨﻮﺳﯽ ﺭﺍ ﻧﺘﻴﺠﻪ ﺑﮕﻴﺮﻳﺪ. ﻣﻨﺒﻊ‬ ‫ﺟﺮﻳﺎﻥ ﻧﺎﺑﺴﺘﻪ ‪ is‬ﺳﻴﻨﻮﺳﯽ ﺍﺳﺖ.) ‪.( iS = 4 cos 2t‬‬ ‫٥‐ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺭﺍﺑﻄﻪ ﻣﺎﺗﺮﻳﺲ ﻫﺎﯼ )‪ B=(1l|F‬ﻭ )‪ Q=(E|1n‬ﺛﺎﺑﺖ ﮐﻨﻴﺪ ﭼﻨﺎﻧﭽﻪ ﺷﺎﺧﻪ ﺩﺭﺧﺘﯽ ﺩﺭ ﺣﻠﻘﻪ ﺍﺳﺎﺳﯽ ﻳﮏ ﻟﻴﻨﮏ‬ ‫ﻭﺍﻗﻊ ﺷﻮﺩ ﺁﻥ ﻟﻴﻨﮏ ﻫﻢ ﺩﺭ ﮐﺎﺕ ﺳﺖ ﺍﺳﺎﺳﯽ ﺁﻥ ﺷﺎﺧﻪ ﺩﺭﺧﺖ ﺣﻀﻮﺭ ﺧﻮﺍﻫﺪ ﺩﺍﺷﺖ.‬ ‫٦‐ ﺍﻟﻒ _ ﭼﺮﺍ ﻣﻮﻟﻔﻪ ﻫﺎﯼ ﺑﺮﺩﺍﺭ ﻭﻟﺘﺎﮊ ﮔﺮﻩ ﻫﺎ ﻧﺴﺒﺖ ﺑﻪ ﮔﺮﻩ ﻣﺒﻨﺎ ﺭﺍ ﻣﯽ ﺗﻮﺍﻥ ﺁﺯﺍﺩﺍﻧﻪ ﺩﺭ ﻳﮏ ﮔﺮﺍﻑ ﺍﺧﺘﻴﺎﺭ ﻧﻤﻮﺩ ؟‬ ‫ﺏ _ ﭼﺮﺍ ﻣﻮﻟﻔﻪ ﻫﺎﯼ ﺑﺮﺩﺍﺭ ﺟﺮﻳﺎﻥ ﻣﺶ ﻫﺎ ﺭﺍ ﻣﯽ ﺗﻮﺍﻥ ﺁﺯﺍﺩﺍﻧﻪ ﺩﺭ ﻳﮏ ﮔﺮﺍﻑ ﺍﺧﺘﻴﺎﺭ ﻧﻤﻮﺩ ؟‬ ‫ﭖ _ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺍﻟﻒ ﻭ ﻳﺎ ﺏ ﺛﺎﺑﺖ ﻧﻤﺎﻳﻴﺪ ﺑﻴﻦ ‪) A‬ﻣﺎﺗﺮﻳﺲ ﺗﻼﻗﯽ ﻣﺨﺘﺼﺮ ﺷﺪﻩ ﮔﺮﻩ ﻫﺎ ﻭ ﺷﺎﺧﻪ ﻫﺎ ( ﻭ ﻣﺎﺗﺮﻳﺲ ‪M‬‬ ‫)ﻣﺎﺗﺮﻳﺲ ﻣﺶ( ﺭﻭﺍﺑﻂ ‪ MAT=o‬ﻭ ‪ AMT=o‬ﺑﺮﻗﺮﺍﺭ ﻣﯽ ﺑﺎﺷﺪ .‬ ‫ﺕ _ ﺁﻳﺎ ﺑﺎ ﺩﺍﻧﺴﺘﻦ ﻣﺎﺗﺮﻳﺲ ‪ M‬ﻣﯽ ﺗﻮﺍﻥ ﻣﺎﺗﺮﻳﺲ ‪ A‬ﺭﺍ ﻳﺎﻓﺖ ؟ ﺑﺎﻟﻌﮑﺲ ﺑﺎ ﺩﺍﻧﺴﺘﻦ ﻣﺎﺗﺮﻳﺲ ‪ A‬ﻣﯽ ﺗﻮﺍﻥ ﻣﺎﺗﺮﻳﺲ ﺭﺍ ‪M‬‬ ‫ﺭﺍ ﻳﺎﻓﺖ ؟ ﺩﺭ ﻫﺮ ﺩﻭ ﻣﻮﺭﺩ ﭼﻨﺪ ﺟﻮﺍﺏ ﺩﺍﺭﻳﻢ ؟‬ ‫ﺻﻔﺤﻪ ٣‬ ‫ﺭﻭﺷﻬﺎﯼ ﺗﺤﻠﻴﻞ ﺣﻠﻘﻪ ﻭ ﮐﺎﺕ ﺳﺖ‬ ‫ﻓﺼﻞ ﺳﻮﻡ‬ ‫ﺑﻌﻨﻮﺍﻥ ﻣﺜﺎﻝ ﺑﺮﺍﯼ 1‪ M‬ﻭ 1‪ A‬ﺯﻳﺮ ﺑﺘﺮﺗﻴﺐ ﺣﺪﺍﻗﻞ ﻳﮏ ﻣﺎﺗﺮﻳﺲ ‪ A‬ﻭ ‪ M‬ﻣﺸﺨﺺ ﮐﻨﻴﺪ.‬ ‫٧‐ ﺍﻟﻒ _ ﺍﺯ ﻣﻌﺎﺩﻻﺕ ‪ KCL‬ﻳﮏ ﮔﺮﺍﻑ ﺩﺭ ﺭﻭﺵ ﺗﺤﻠﻞ ﮔﺮﻩ )‪ (Aj=o‬ﻭ ﺗﺤﻠﻴﻞ ﺣﻠﻘﻪ )‪ ( j=BTi‬ﺭﺍﺑﻄﻪ ﻣﺎﺗﺮﻳﺲ ﻫﺎﯼ ‪ A‬ﻭ‬ ‫‪ B‬ﺭﺍ ﻧﺘﻴﺠﻪ ﺑﮕﻴﺮﻳﺪ . ﻫﻤﻴﻦ ﺭﺍﺑﻄﻪ ﺭﺍ ﺍﺯ ﻣﻌﺎﺩﻻﺕ ‪ KVL‬ﮔﺮﺍﻑ ﺩﺭ ﺭﻭﺵ ﺗﺤﻠﻴﻞ ﮔﺮﻩ )‪ ( v=ATe‬ﻭ ﺗﺤﻠﻴﻞ ﺣﻠﻘﻪ‬ ‫)‪ (Bv=o‬ﺑﻴﺎﺑﻴﺪ .‬ ‫ﺏ _ ﺭﺍﺑﻄﻪ ﻣﺎﺗﺮﻳﺲ ﻣﺶ ‪ M‬ﻭ ﻣﺎﺗﺮﻳﺲ ﮐﺎﺕ ﺳﺖ ﺍﺳﺎﺳﯽ ‪ Q‬ﻳﮏ ﮔﺮﺍﻑ ﺍﺯ ﻣﻌﺎﺩﻻﺕ ‪ KCL‬ﻳﺎ ‪ KVL‬ﻧﺘﻴﺠﻪ ﺑﮕﻴﺮﻳﺪ.‬ ‫ﭖ _ ﺗﻌﺪﺍﺩ ﺩﺭﺧﺖ ﻫﺎﯼ ﻳﮏ ﮔﺮﺍﻑ ‪ N‬ﺍﺯ ﺭﺍﺑﻄﻪ ]‪ N=Det[AAT‬ﻣﺤﺎﺳﺒﻪ ﻣﯽ ﺷﻮﺩ. ﺑﺮﺍﯼ ﮔﺮﺍﻑ ﺷﮑﻞ ﺏ ﻣﺴﺌﻠﻪ ٢ﺩﺭﺳﺘﯽ‬ ‫ﺁﻧﺮﺍ ﺑﺮﺭﺳﯽ ﻧﻤﺎﺋﻴﺪ.‬ ‫٨‐ﺩﺭ ﮔﺮﺍﻑ ﻣﻘﺎﺑﻞ:‬ ‫ﺍﻟﻒ _ ﺩﺭﺧﺘﯽ ﺍﺧﺘﻴﺎﺭ ﻧﻤﺎﺋﻴﺪ ﮐﻪ ﮐﺎﺕ ﺳﺖ ﻫﺎﯼ )٦،٤،٣،١( ﻭ‬ ‫)٨،٦،٥،٤( ﺟﺰﺀ ﮐﺎﺕ ﺳﺖ ﻫﺎﯼ ﺍﺳﺎﺳﯽ ﺁﻥ ﻭ )٧،٥،٢،٦،١(‬ ‫ﻳﮏ ﺣﻠﻘﻪ ﺍﺳﺎﺳﯽ ﺁﻥ ﺑﺎﺷﺪ . ﭘﺲ ﺍﺯ ﺗﻌﻴﻴﻦ ﺩﺭﺧﺖ ﻫﻤﻪ ﮐﺎﺕ‬ ‫ﺳﺖ ﻫﺎ ﻭ ﺣﻠﻘﻪ ﻫﺎﯼ ﺍﺳﺎﺳﯽ ﺩﻳﮕﺮ ﺭﺍ ﻣﺸﺨﺺ ﻧﻤﺎﻳﻴﺪ.‬ ‫ﺏ _ ﺗﻤﺎﻡ ﺩﺭﺧﺖ ﻫﺎﻳﯽ ﮐﻪ ﺷﺎﺧﻪ ﻫﺎﯼ ١ﻭ٤ﻭ٦ ﺟﺰﺀ ﻟﻴﻨﮏ ﻫﺎﯼ ﺁﻥ‬ ‫ﺑﺎﺷﻨﺪ ، ﻣﺸﺨﺺ ﻧﻤﺎﻳﻴﺪ.‬ ‫ﭖ _ ﺗﻤﺎﻡ ﺩﺭﺧﺖ ﻫﺎﻳﯽ ﮐﻪ ﺷﺎﺧﻪ ﻫﺎﯼ ١ﻭ٤ﻭ٦ ﺟﺰﺀ ﺷﺎﺧﻪ ﻫﺎﯼ‬ ‫ﺩﺭﺧﺖ ﺑﺎﺷﻨﺪ ، ﻣﺸﺨﺺ ﻧﻤﺎﻳﻴﺪ.‬ ‫٩ ‐ ﺍﻟﻒ _ ﺩﺭ ﮔﺮﺍﻑ ﻫﺎﯼ ﺯﻳﺮ ﺩﺭﺧﺘﯽ ﺍﺧﺘﻴﺎﺭ ﻧﻤﺎﻳﻴﺪ ﮐﻪ ﮐﺎﺕ ﺳﺖ ﻫﺎﯼ ﺍﺳﺎﺳﯽ ﺁﻥ ﻫﻤﺎﻥ ﺷﺎﺧﻪ ﻫﺎﯼ ﻭﺻﻞ ﺷﺪﻩ ﺑﻪ ﮔﺮﻩ ﻫﺎ‬ ‫ﺑﺎﺷﻨﺪ . )ﻫﻤﻪ ﺟﻮﺍﺏ ﻫﺎ ( .‬ ‫ﺏ _ ﺩﺭ ﮔﺮﺍﻑ ﻫﺎﯼ ﺯﻳﺮ ﺩﺭﺧﺘﯽ ﺍﺧﺘﻴﺎﺭ ﻧﻤﺎﻳﻴﺪ ﮐﻪ ﺣﻠﻘﻪ ﻫﺎﯼ ﺍﺳﺎﺳﯽ ﺁﻥ ﻫﻤﺎﻥ ﻣﺶ ﻫﺎ ﺑﺎﺷﻨﺪ )ﻫﻤﻪ ﺟﻮﺍﺏ ﻫﺎ ( . ﺩﺭ ﭼﻪ‬ ‫ﮔﺮﺍﻑ ﻫﺎﻳﯽ ﺍﻟﻒ ﻳﺎ ﺏ ﺟﻮﺍﺏ ﻧﺪﺍﺭﺩ ؟‬ ‫ﺻﻔﺤﻪ ٤‬ ‫ﺭﻭﺷﻬﺎﯼ ﺗﺤﻠﻴﻞ ﺣﻠﻘﻪ ﻭ ﮐﺎﺕ ﺳﺖ‬ ‫ﻓﺼﻞ ﺳﻮﻡ‬ ‫٠١‐ ﺩﺭ ﮔﺮﺍﻑ ﻣﻘﺎﺑﻞ ﺩﺭﺧﺖ )ﻳﺎ ﺩﺭﺧﺖ ﻫﺎ ﻳﯽ (ﻣﺸﺨﺺ ﻧﻤﺎﻳﻴﺪ ﮐﻪ‬ ‫ﻳﮏ ﺣﻠﻘﻪ ﺍﺳﺎﺳﯽ ﺁﻥ )‪ (d،c،b‬ﻭ ﻳﮏ ﮐﺎﺕ ﺳﺖ ﺍﺳﺎﺳﯽ ﺁﻥ‬ ‫)‪( h،e،b،c،k‬ﺑﺎﺷﺪ . ﻫﻤﻪ ﺟﻮﺍﺏ ﻫﺎﯼ ﻣﻤﮑﻦ ﺭﺍ ﻣﺸﺨﺺ ﻧﻤﺎﻳﻴﺪ.‬ ‫١١‐ ﺭﺍﺑﻄﻪ ﻣﺎﺗﺮﻳﺲ ﺣﻠﻘﻪ ﺍﺳﺎﺳﯽ ‪ B‬ﻭ ﻣﺎﺗﺮﻳﺲ ﮐﺎﺕ ﺳﺖ ﺍﺳﺎﺳﯽ ‪ Q‬ﭼﻴﺴﺖ ؟ ﻭ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺁﻥ ﺛﺎﺑﺖ ﮐﻨﻴﺪ ﭼﻨﺎﻧﭽﻪ ﻳﮏ‬ ‫ﻟﻴﻨﮏ ﺩﺭ ﮐﺎﺕ ﺳﺖ ﺍﺳﺎﺳﯽ ﻳﮏ ﺷﺎﺧﻪ ﺩﺭﺧﺖ ﺑﺎﺷﺪ ، ﺁﻥ ﺷﺎﺧﻪ ﺩﺭﺧﺖ ﻧﻴﺰ ﺩﺭ ﺣﻠﻘﻪ ﺍﺳﺎﺳﯽ ﺁﻥ ﻟﻴﻨﮏ ﺣﻀﻮﺭ ﺩﺍﺭﺩ .‬ ...
View Full Document

This note was uploaded on 02/06/2011 for the course ECE 423 taught by Professor Dolatabadi during the Spring '11 term at Amirkabir University of Technology.

Ask a homework question - tutors are online